Anyone knowledgeable about fiberglass?

I haven't done much myself; just some glass/epoxy repairs here and there. Most of my "knowledge" comes from kayaks.
But my understanding is that the glass gives it all the strength; the resin is just to hold the glass together. On kayaks they suck as much resin out as they can, leaving just enough to keep the glass wet, on the theory that any extra resin makes it heavier and more brittle without doing anything to make it better.

My neighbor makes custom fiberglass fabrications; chiefly things like boat hatches. He tells me that everything I think I know is wrong. He works only in polyester because it is more rigid. He says that all the strength comes from the resin; the glass is just there to make the resin less brittle.
Kayaks are kind of an exception; there the strength comes from the shape.
Minimal resin is used because low weight is more important than fiberglass strength.

He must know what he is talking about because he is reasonably successful; but it is so so different from everything else I have heard that I don't know what to make of it.

Any comments that would help me here?

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You're both right and wrong, depending on what you're goal is. The glass and resin work hand in hand to make EACH OTHER stronger. I can wrap glass around an air tank without resin, fill the air tank, and watch the glass shred while the tank expands. Similarly I can paint a thick band of resin around the tank (no glass) and watch it crack as the tank expands.
Put the glass and the resin together though and I'll have to pump the crap out of the tank to blow the glass band.

That being said however, pouring boatloads of resin on a single layer of glass won't lock the glass stitching together any better than a thinner layer. It will stiffen it up though to carry more weight without flexing as much... if that's your goal.

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So if you need a stiff structure, a lot of resin is good. If stiffness is secondary to weight, then little resin is desirable.

But lets say you have a thin panel made with little resin that isn't stiff enough for your need. You could stiffen it by using more resin, buut couldn't you also stiffen it by using a little more glass and a little more resin; or is bulking up with just resin more effective?

buut couldn't you also stiffen it by using a little more glass and a little more resin; or is bulking up with just resin more effective?

Both, depending on your construction methods. Ideally what you want is a thick layer of resin sandwiched between a couple of layers of glass. The glass on either side will resist flexing in on itself (one layer will resist flex in one direction while the other layer resists flex in the opposing direction) while the resin provides the separation required for the glass to do its job. Because one side has to flex more than the other in order for a deflection to take place, the thicker the resin the more the glass layers are separated and the more the outside layer of glass must flex for a smaller bend. A bit hard to explain, but consider it like a car where the outside wheel has to turn faster than the inside wheel. The further apart the wheels are then the faster the outside wheel has to go.

Both, depending on your construction methods. Ideally what you want is a thick layer of resin sandwiched between a couple of layers of glass. The glass on either side will resist flexing in on itself (one layer will resist flex in one direction while the other layer resists flex in the opposing direction) while the resin provides the separation required for the glass to do its job. Because one side has to flex more than the other in order for a deflection to take place, the thicker the resin the more the glass layers are separated and the more the outside layer of glass must flex for a smaller bend. A bit hard to explain, but consider it like a car where the outside wheel has to turn faster than the inside wheel. The further apart the wheels are then the faster the outside wheel has to go.

Kayaks will use sandwichs of glass-foam-glass where stiffness and lightweight is necessary. Where weight is not important glass-resin-glass is cheaper; is that the idea?

So glass IS the major strength component, but the extra resin gives it stiffness?